A344007 Denominators of triangle formed by beginning with 1 on row 1, then producing row n by replacing the largest value on row n-1, k, by 1/n and k - 1/n, and arranging the entries in order from smallest to largest.
1, 2, 2, 6, 3, 2, 6, 4, 4, 3, 15, 6, 5, 4, 4, 12, 15, 6, 6, 5, 4, 12, 28, 15, 7, 6, 6, 5, 40, 12, 28, 8, 15, 7, 6, 6, 18, 40, 12, 28, 9, 8, 15, 7, 6, 18, 15, 40, 12, 10, 28, 9, 8, 15, 7, 77, 18, 15, 40, 12, 11, 10, 28, 9, 8, 15, 20, 77, 18, 15, 40, 12, 12, 11, 10, 28, 9, 8
Offset: 1
Examples
The triangle's first 10 rows: 1 1/2, 1/2 1/6, 1/3, 1/2 1/6, 1/4, 1/4, 1/3 2/15, 1/6, 1/5, 1/4, 1/4 1/12, 2/15, 1/6, 1/6, 1/5, 1/4 1/12, 3/28, 2/15, 1/7, 1/6, 1/6, 1/5 3/40, 1/12, 3/28, 1/8, 2/15, 1/7, 1/6, 1/6 1/18, 3/40, 1/12, 3/28, 1/9, 1/8, 2/15, 1/7, 1/6 1/18, 1/15, 3/40, 1/12, 1/10, 3/28, 1/9, 1/8, 2/15, 1/7 ... The denominators are: 1 2, 2, 6, 3, 2, 6, 4, 4, 3, 15, 6, 5, 4, 4, 12, 15, 6, 6, 5, 4, ...
Programs
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PARI
lista(nn) = {my(row, nrow, drow); for (n=1, nn, if (n==1, row = [1], k = vecmax(row); nrow = row; nrow[n-1] = 1/n; nrow = concat(nrow, k - 1/n); row = vecsort(nrow);); drow = apply(denominator, row); for (k=1, #drow, print1(drow[k], ", ")););} \\ Michel Marcus, Jun 09 2021
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